indeed in liveview it works, all be it very slow and the target needs to have a fair bit of contrast.

Live view will focus even way outside the limits. I've used it to focus (outdoors on a sunny day) with a 70-300L (4-5.6) and a 3x extender at the 300 end (f/16.8, effectively). No sweat. Just a little slow (and by that, I mean painfully slow, but that's live view for you).

A Canon 12mm tube isn't cheap and I don't know how reliable the el cheapo ones are so I don't want to do an experiment myself.

So what do you think would give the better image:

A good f/2.8 lens with a 2xTC at f/5.6 on a 7d (e.g. the f/2.8 300mm II + the 2xTC III)?Or the same lens plus 1.4x and 2xTC at f/8 on a 5D III?

Both have a similar reach.

There is no glass in the 12mm tube. I have an el cheapo and it works find. Mind it wasn't that cheap. Having had all that kit I wouldn't hesitate to recommend the 5D3. In fact I think you will find that the 5d3 + 2xTC + 300mm f2.8 will give just as much reach as the 7D + 2xTC + 300mm f2.8 because you can crop harder for the same IQ. And of course you will still have the 1.4TC to add for a bit more reach.

Not everyone will agree with this and will be convinced that the greater pixel desity of the 7D will make up for the improved IQ of the 5D3. Guess what I won't lose sleep over their opinion.

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If you debate with a fool onlookers can find it VERY difficult to tell the difference.

No need to do the experiment. I took out both my 5DIII and 7D yesterday to test in the wild in a nature reserve. I had forgotten how slowly the 7D focusses with the 300mm f/2.8 II with the 2xTC attached. Whereas the 7D is fine with the native lens, it is painfully slow with the 2xTC III attached. So, I might get a cheaper 12mm ring for the fun of it ot see what it does.

Very cool, but let me ask this: Is this combo getting you better results than just cropping? I'm not saying it is not, but that is the thing about a teleconverter, or combination of converters is it has to outperform just cropping the image.

If you shoot the moon with just the 2.0X and then crop, is there less less detail?

After reading the original post I gave it a try just for fun. And yes the results were really quite good and better than cropping.

When you think about it, it seems almost self-evident that shooting at the higher magnification would provide better results than cropping in to an image taken at smaller magnification - ignoring for the moment any IQ issues induced soley by higher magnification such as camera shake or shallow DOF. With those other variables under control, the higher magnification has to produce an image of more exquisite detail.

For any given detail in the image - a crater for example - doubling the magnification will increase the number of pixels used to image that detail by a factor of 4.

Let's take a hypothetical. Assume I shoot an image of the moon with a 400mm lens and one of the craters in that image takes up a matrix of pixels on the sensor measuring 50X50 pixels, for a total of 2500 pixels. Now I want to increase the apparent size of that crater by cropping in to the image to give an angle of view equal to what I would have had if I'd shot with an 800mm lens. Even though I have doubled size of that portion of the image in each dimension, I still haven't increased the number of sensor pixels contributing to that part of the image so there is no additional detail to be garnered.

However, if I had taken the image with an 800mm lens to begin with, that portion of the image would be twice as large on the sensor than the previous shot, measuring 100X100 pixels. Because of the squaring effect, there are now 100X100, or 10000 pixels contributing detail for that same portion of the image. The uncropped image will be similar in angle of view to the previous cropped image, but will have a much higher pixel density and thus much higher resolving power vis-a-vis the image details.

When you think about it, it seems almost self-evident that shooting at the higher magnification would provide better results than cropping in to an image taken at smaller magnification - ignoring for the moment any IQ issues induced soley by higher magnification such as camera shake or shallow DOF. With those other variables under control, the higher magnification has to produce an image of more exquisite detail.

What about any IQ issues introduced by the process of magnification, itself? Specifically, I would bet that cropping an image would yield results superior to increasing magnification with a crappy TC.

When you think about it, it seems almost self-evident that shooting at the higher magnification would provide better results than cropping in to an image taken at smaller magnification - ignoring for the moment any IQ issues induced soley by higher magnification such as camera shake or shallow DOF. With those other variables under control, the higher magnification has to produce an image of more exquisite detail.

What about any IQ issues introduced by the process of magnification, itself? Specifically, I would bet that cropping an image would yield results superior to increasing magnification with a crappy TC.

I believe I mentioned IQ issues related to magnification itself..."ignoring for the moment any IQ issues induced soley by higher magnification such as camera shake or shallow DOF. With those other variables under control, the higher magnification has to produce an image of more exquisite detail."

With that caveat, I didn't think it necessary to go through every single magnification-related variable that might affect IQ, with a crappy TC being one of the possibilities. Looks the OP is invested in top of line L-series lenses and TCs, so I'm commenting on the assumption that crappy gear isn't a factor.

Therefore my analysis was limited strictly to the difference in detail resolution based on pixel density in the image, when comparing an image that is cropped to yield the same image that shooting at a natively higher magnification would yield.

You are, of course, correct that a quality longer lens gives better resolution than a quality shorter one, all things being equal. What we want to know is whether stacking TCs on to a particular lens does lower its IQ to such an extent that it negates the gain in focal length. The series II telephotos and series III TCs are beautifully designed to work well together. In my experience that is so but adding a 1.4 to a 100-400 is no better than using PS to increase size by 1.4x. What I particularly want to know is the IQ effect on stacking two series III together. Why did Canon stop us doing that? Was it intentional or what? My 5D III froze when I stacked a Kenko 1.4 TC onto a 2xTC III and a 300mm f/2.8 II.